📄 ch11_3_1.htm
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<! Made by Html Translation Ver 1.0><html><head><title> 微分 </title></head><body BACKGROUND="../img1/bg0000.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img/bg0000.gif"><script language="JAVASCRIPT"><!--if (navigator.onLine){document.write("<!-- Spidersoft WebZIP Ad Banner Insert -->");document.write("<TABLE width=100% border=0 cellpadding=0 cellspacing=0>");document.write("<TR>");document.write("<TD>");document.write("<ILAYER id=ad1 visibility=hidden height=60></ILAYER>");document.write("<NOLAYER>");document.write("<IFRAME SRC='http://www.spidersoft.com/ads/bwz468_60.htm' width=100% height=60 marginwidth=0 marginheight=0 hspace=0 vspace=0 frameborder=0 scrolling=no></IFRAME>");document.write("</NOLAYER>");document.write("</TD>");document.write("</TR>");document.write("</TABLE>");document.write("<!-- End of Spidersoft WebZIP Ad Banner Insert-->");} //--></script><!-- Spidersoft WebZIP Ad Banner Insert --><!-- End of Spidersoft WebZIP Ad Banner Insert--><font COLOR="#0000FF"><h1>11.3.1 微分</h1></font><hr><p><font COLOR="#FF0000" FACE="Times New Roman">diff</font>函数用以演算一函数的微分项，相关的函数语法有下列<font FACE="Times New Roman">4</font>个： </p><p><font COLOR="#FF0000" FACE="Times New Roman">diff(f) </font>传回<font COLOR="#FF0000" FACE="Times New Roman">f</font>对预设独立变数的一次微分值 </p><p><font COLOR="#FF0000" FACE="Times New Roman">diff(f,</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">t</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">)</font><font FACE="Times New Roman"> </font>传回<font COLOR="#FF0000" FACE="Times New Roman">f</font>对独立变数<font COLOR="#FF0000" FACE="Times New Roman">t</font>的一次微分值 </p><p><font COLOR="#FF0000" FACE="Times New Roman">diff(f,n)</font><font FACE="Times New Roman"> </font>传回<font COLOR="#FF0000" FACE="Times New Roman">f</font>对预设独立变数的<font COLOR="#FF0000" FACE="Times New Roman">n</font>次微分值 </p><p><font COLOR="#FF0000" FACE="Times New Roman">diff(f,</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">t</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">,n)</font><font FACE="Times New Roman"> </font>传回<font COLOR="#FF0000" FACE="Times New Roman">f</font>对独立变数<font COLOR="#FF0000" FACE="Times New Roman">t</font>的<font COLOR="#FF0000" FACE="Times New Roman">n</font>次微分值 <br></p><p>因为之前再第八章介绍的数值微分函数也是用<font COLOR="#FF0000" FACE="Times New Roman">diff</font>，因此这个函数是靠输入的引数决定是以数值或是符号 微分，如果引数为向量则执行数值微分，如果引数为符号表示式则执行符号微分。 <br></p><p>先定义下列三个方程式，接著再演算其微分项： </p><p><font COLOR="#FF0000" FACE="Times New Roman">>>S1 = </font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">6*x^3-4*x^2+b*x-5</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">;</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>>S2 = </font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">sin(a)</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">;</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>>S3 = </font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">(1 - t^3)/(1 + t^4)</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">; <br></font></p><p><font COLOR="#FF0000" FACE="Times New Roman">>>diff(S1)</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">18*x^2-8*x+b</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>>diff(S1,2)</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">36*x-8</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>>diff(S1,</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">b</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">)</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">x</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>>diff(S2)</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">cos(a)</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>>diff(S3)</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">-3*t^2/(1+t^4)-4*(1-t^3)/(1+t^4)^2*t^3</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">>>simplify(diff(S3))</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p><p><font COLOR="#FF0000" FACE="Times New Roman">t^2*(-3+t^4-4*t)/(1+t^4)^2</font></p><hr><a HREF="ch11_3.htm" tppabs="http://webclass.ncu.edu.tw/~junwu/ch11_3.htm"><p><img SRC="../img1/lastpage.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img/lastpage.gif" BORDER="0" WIDTH="42" HEIGHT="42"></a> <a HREF="ch11_3_2.htm" tppabs="http://webclass.ncu.edu.tw/~junwu/ch11_3_2.htm"><img SRC="../img1/nextpage.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img/nextpage.gif" BORDER="0" HSPACE="10" WIDTH="42" HEIGHT="42"></a> <a HREF="../index.html" tppabs="http://webclass.ncu.edu.tw/~junwu/index.html"><img SRC="../img1/outline.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img/outline.gif" BORDER="0" HSPACE="6" WIDTH="42" HEIGHT="42"></a><br><font SIZE="2" COLOR="#AA55FF">上一页 下一页 讲义大纲 </font><layer src="http://www.spidersoft.com/ads/bwz468_60.htm" visibility="hidden" id="a1" width="600" onload="moveToAbsolute(ad1.pageX,ad1.pageY); 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